Tibetan singing bowls: levitation via resonance

The dynamics of fluid-filled Tibetan bowls was the  research subject of Denis Terwagne during his internship in the Applied Math Lab. Our combined experimental and theoretical investigation elucidated the manner in which the rubbing of the bowl excites its resonant wave modes, which in turn excite Faraday waves on the fluid surface that may break, giving rise to the ejection of droplets that bounce in place or skip across the free surface.

See paper here: Terwagne & Bush (2011)


And he showed Pierre a globe, a quivering ball of no dimensions, its surface consisting of drops tightly packed together. The drops moved and shifted, now merging from several into one, now dividing from one into many. Each drop strove to spread and take up the most space, but the others, striving to do the same, pressed against it, sometimes destroying, sometimes merging.  “This is life”, said the old teacher. “In the center is God, and each drop strives to expand in order to reflect Him in the greatest measure. It grows, merges and shrinks, is obliterated on the surface, vanishes into the depths, then resurfaces.”   – Leo Tolstoy, War and Peace, 1865


SELECT PRESS:  Nature News Blog , BBC News , UniverScience , Sciences et Sante

Biomimicry and the culinary arts

Edible flowers assist in the drinking of fine, palate-cleansing liqueurs.

The group is collaborating with cutting-edge Spanish chef Jose Andres at the margins of science and the culinary arts.Two of our biomimetic inventions are being explored and developed by his ThinkFood group.

Inspired by a family of floating flowers, the edible flower (image at right) provides a mean of drinking small volumes of fluid in an elegant fashion.

Inspired by a means of propulsion used by a class of water-walking insects, cocktail boats (image below) propel themselves by generating a fore-aft chemical gradient.

Both designs developed by Lisa Burton and Nadia Cheng.


The cocktail boat

The aerodynamics of the beautiful game

The dynamics of sports is a subject familiar to many, a rich area of application of  mathematical modeling. The dynamics of footballs in flight has been the subject of  a recent article, and we have a continuing interest in this class of problems through our interaction with Christophe Clanet.

PAPER:  Bush (2013)

PRESS:  Le Progres – Lyons 2009 , MIT News 2014 , America24 , Wall Street Journal

In the video below we see Karl Suabedissan striking two balls, one smooth, the other identical but for an elastic band wrapped around its equator. Both balls are struck with his instep so as to impart a spin that is counterclockwise as viewed from above, so one expects them to bend from right to left. However, the smooth ball bends in precisely the opposite sense. The presence of the surface roughness in the form of the elastic band is sufficient to change the boundary layer on the ball surface from laminar to turbulent, thus restoring the sign of the expected spin-induced lateral force on the ball. It is thus that all footballs have some surface roughness; otherwise, they would bend the wrong way.

The dynamics of rolling ribbons

We present the results of a combined experimental and theoretical investigation of rolling elastic ribbons. Particular attention is given to characterizing the steady shapes that arise in static and dynamic rolling configurations. In both cases, above a critical value of the forcing (either gravitational or centrifugal), the ribbon assumes a two-lobed, peanut shape similar to that assumed by rolling droplets. Our theoretical model allows us to rationalize the observed shapes through consideration of the ribbon’s bending and stretching in response to the applied forcing.

See paper here: Raux, Reis, Bush & Clanet_2010

PRESS:  MIT News , Science NOW

The elastochrone: rolling on a bending beam

We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler– Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favourably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is shown to exceed the classical brachistochrone, the shortest time between two points in a gravitational field.

See paper here: Aristoff, Clanet and Bush (2009)

Rocking and rolling down an incline

The snail cylinder rolls down an incline at a snail's pace.

We consider the dynamics of a hollow cylindrical shell that is filled with viscous fluid and another, nested solid cylinder, and allowed to roll down an inclined plane. A mathematical model is compared to simple experiments. Two types of behaviour are observed experimentally: on steeper slopes, the device accelerates; on shallower inclines, the cylinders rock and roll unsteadily downhill, with a speed that is constant on average. The theory also predicts runaway and unsteady rolling motions. For the rolling solutions, however, the inner cylinder cannot be suspended in the fluid by the motion of the outer cylinder, and instead falls inexorably toward the outer cylinder. Whilst ‘contact’ only occurs after an infinite time, the system slows progressively as the gap between the cylinders narrows, owing to heightened viscous dissipation. Such a deceleration is not observed in the experiments, suggesting that some mechanism limits the approach to contact. Coating the surface of the inner cylinder with sandpaper of different grades changes the rolling speed, consistent with the notion that surface roughness is responsible for limiting the acceleration.

See paper here:  Balmforth, Bush, Vener & Young (2007)